Author
Fawang Liu
Other affiliations: Xiamen University, Changsha University of Science and Technology, Fuzhou University ...read more
Bio: Fawang Liu is an academic researcher from Queensland University of Technology. The author has contributed to research in topics: Fractional calculus & Numerical analysis. The author has an hindex of 63, co-authored 335 publications receiving 15138 citations. Previous affiliations of Fawang Liu include Xiamen University & Changsha University of Science and Technology.
Papers published on a yearly basis
Papers
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TL;DR: In this article, a space fractional Fokker-Planck equation (SFFPE) with instantaneous source is considered, and a numerical scheme for solving SFFPE is presented.
699 citations
TL;DR: Using mathematical induction, it is proved that the IDM is unconditionally stable and convergent, but the EDM is conditionally stable and Convergent.
514 citations
TL;DR: In this article, the Riesz fractional diffusion equation (RFDE) and RFADE (RFADE) were considered and analytic solutions of both the RFDE and the RFADE were derived.
511 citations
TL;DR: In this paper, a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain with explicit and implicit Euler approximations is considered.
Abstract: In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moveover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.
478 citations
TL;DR: An anomalous subdiffusion equation (ASub-DE) is considered and a new implicit numerical method (INM) and two solution techniques for improving the order of convergence of the INM for solving the ASub-DE are proposed.
Abstract: A physical-mathematical approach to anomalous diffusion is based on a generalized diffusion equation containing derivatives of fractional order. In this paper, an anomalous subdiffusion equation (ASub-DE) is considered. A new implicit numerical method (INM) and two solution techniques for improving the order of convergence of the INM for solving the ASub-DE are proposed. The stability and convergence of the INM are investigated by the energy method. Some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and supporting theoretical results can also be applied to other fractional integro-differential equations and higher-dimensional problems.
357 citations
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01 Jan 2015
3,828 citations
TL;DR: It is proved that the full discretization is unconditionally stable, and the numerical solution converges to the exact one with order O(@Dt^2^-^@a+N^- ^m), where @Dt,N and m are the time step size, polynomial degree, and regularity of the exact solution respectively.
1,420 citations
TL;DR: In this paper, the authors developed practical numerical methods to solve one dimensional fractional advection-dispersion equations with variable coefficients on a finite domain and demonstrated the practical application of these results is illustrated by modeling a radial flow problem.
1,334 citations
TL;DR: The Thermophysical Properties Research Literature Retrieval Guide as discussed by the authors was published by Y. S. Touloukian, J. K. Gerritsen and N. Y. Moore.
Abstract: Thermophysical Properties Research Literature Retrieval Guide Edited by Y. S. Touloukian, J. K. Gerritsen and N. Y. Moore Second edition, revised and expanded. Book 1: Pp. xxi + 819. Book 2: Pp.621. Book 3: Pp. ix + 1315. (New York: Plenum Press, 1967.) n.p.
1,240 citations